InterviewSolution
Saved Bookmarks
InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 7602. |
Which of the following options is the only CORRECT combination ? |
|
Answer» (I) (i) (Q) |
|
| 7603. |
Which of the following options is the only CORRECT combination ? |
|
Answer» <P>(II) (i) (S) |
|
| 7604. |
A and B are centers of two circles that touch each other externally, as shown in the figure.What is the area of the circle whose diameter is AB? |
| Answer» ANSWER :B | |
| 7605. |
For a Poisson veriate X , if P(X = 2) = 3 P(X = 3) then the mean of X is |
|
Answer» 1 |
|
| 7606. |
The sum of the series 0.4 + 0.004 + 0.00004 + infty is |
|
Answer» `11/25` |
|
| 7607. |
A variable plane passes through a fixed point (1,-2,3)and meets the coordinates axes at points A,B, C then the point of intersection of the planes thorugh A,B ,Cparallel to the coordinates planes lies on |
|
Answer» ` xy- (1//2)YZ +(1//3) ZX =6` |
|
| 7608. |
Obtain the following integrals : int (3x-1)/(sqrt(x^(2)+9))dx |
|
Answer» |
|
| 7609. |
A school awarded 38 medals in football, 15 in basketball and 20 in cricket. Suppose these medals went to a total of 58 students and only three students got medals in all three sports. If only 5 students got medals in football and basketball, then the number of medals received in exactly two of three sports is |
|
Answer» 7 |
|
| 7610. |
Ifalpah , beta , gammaare therootsof the equationx^3 + qx +r=0 find thevalueof ( beta- gamma)^2 +( gamma- alpha)^2+(alpha- beta)^2 |
|
Answer» |
|
| 7611. |
Show that the lines (x-5)/(7)=(y+2)/(-5)=z/1 and x/1=y/2=z/3 are perpendicular to each other. |
|
Answer» |
|
| 7612. |
If the straight lines joining origin to the points of intersection of the line x+y=1 with the curve x^2+y^2 +x-2y -m =0are perpendicular to each other , then the value of m should be |
|
Answer» `-1/2` |
|
| 7613. |
If x_1 and x_2 (x_2gtx_1) are the integral solutions of the equation (log_5x)^2+log_(5x)(5/x)=1, , the value of |x_2-4x_1| is |
|
Answer» |
|
| 7614. |
{:(,"Hyperbola point ",,"Pole"),(I,3x^(2)-4y^(2) =12-3x+2y+6=0",", ,(a) ("2,-3")),(II,x^(2) -3y^(2) =32x + y-1=0",",,(b) ("-1,-3")),(III,3x^(2) -5y^(2) =15-2x+5y-5=0"," ,,(c) (-2,1)) ,(IV,9x^(2) -16y^(2) =144-3x-16y+48=0",",,(d) ("6,-1")):} |
|
Answer» a,b,c,d |
|
| 7615. |
Evaluate the following integrals int_(0)^((41)/(2)) e^(2x-{2x})dx where [] denotes the GIF |
|
Answer» |
|
| 7616. |
Write the value x for which d/dxsin^-1(sin x)=1 |
| Answer» SOLUTION :`d/dxsin(sin^-1x)=1` for `X in (-pi/2,pi/2)` | |
| 7617. |
From the top of a hill h meters high the angle of depressions of the top and the bottem of a piller are alpha " and "beta respectively. The height (in meters) of the piller is |
|
Answer» `(H(TAN BETA- tan ALPHA))/(tan beta)` |
|
| 7618. |
If A and B are two events such that P(A uu B)=0.65, P(A nnB)=0.15 then P(barA)+P(barB)= |
|
Answer» |
|
| 7619. |
P is the point of contact of the tangent from the origin to the curve y=log_(e)x The length of the perpendicular drawn from the origin to the normal at p is |
|
Answer» `1/E` |
|
| 7620. |
If a and b are respectively the internal and external bisectors of the angles between the vetors-hati + 2 hatj - 2 hatk " and " 3 hati + 4 hatj " and " |a| = 2/3 sqrt6, | b | = 2/3 sqrt3 , then one of the values of a-b is |
|
Answer» `1/10(-8hati + 11 HATJ - 2 hatk)` |
|
| 7621. |
If a triangle is chosen at random inscribed in a fixed circle and if the probability tha the orthocentre lies inside circumcircle is (1)/(x) then x equals __________ |
|
Answer» |
|
| 7622. |
int(x^5dx)/((x^2+x+1)(x^6+1)(x^4-x^3+x-1))= |
|
Answer» `log_e|(x^6-1)/(x^6+1)|+C` |
|
| 7623. |
Loucus of complex number satifyingare arg[(z-5+4i)//(z+3-2i)] = - pi//4 is the are of a circle |
|
Answer» whose radiusis `5sqrt(2)`  `(z_(0) - (-3+2i))/(z_(0)-(5-4i))= (BD)/(AD)e^(ipi//2)=i` `RARR z_(0) +3-2i =iz_(0) - 5i -4` `rArr z_(0) = - 2-5i` `rArr " Radius" AD = |5-4i-(-2-5i)|` `= |7+i|` `= sqrt(50) = 5sqrt(2)` Length of arc `= (3)/(4)` (Perimeter of circle) `=(3)/(4)(2pixx5sqrt(2))` `= (15)/(sqrt(2))` |
|
| 7624. |
Choose the correct answer The rate of change of the area of a circle w.r.t its radius r at r = 6 cm is. |
|
Answer» `10PI` |
|
| 7625. |
Ifalpha, beta , gammaare therootsofx^3 +2x^2 +3x +8=0then(3-alpha )(3 - beta) (3-gamma)= |
|
Answer» 52 |
|
| 7626. |
If X is a random varibale with probability distribution P(X = k) = ((k+1)C)/(2), K = 0, 1, 2,…. then find C. |
|
Answer» |
|
| 7628. |
If e_(1) is the eccentricity of the ellipse x^(2)/16+y^(2)/25=1 and e_(2) is the eccentricity of a hyperbola passing through the foci of the given ellipse and e_(1)e_(2)=1, then the equation of such a hyperbola among the following is |
|
Answer» `x^(2)/(16)+y^(2)/(25)=1` |
|
| 7629. |
If a,b,c are the sides of a Delta ABC, which are in A.P.,then cot"" ( C )/( 2) equals : |
|
Answer» `3 tan "" ( A)/(2)` |
|
| 7630. |
What is the smallest positive integer k such that k(3^(3) + 4^(3)+ 5^(3)+ 6^(3)) = a^nfor some positive integer a andn with n gt 1 ? |
|
Answer» |
|
| 7631. |
[{:((1)/(25),0),(x,(1)/(25)):}]=[{:(5,0),(-a,5):}]^(-2)then x =……….. |
|
Answer» `(a)/(125)` |
|
| 7633. |
2i xx (3i - 4k) + (I + 2j) xx k = |
| Answer» | |
| 7634. |
If x is real, the minimum value of x^(2)-8x+17 is : |
|
Answer» 2 |
|
| 7635. |
Different words are being formed by arranging the letters of the word "SUCCESS". The probability of selecting a word that begins and ends with S is |
|
Answer» `1/7` |
|
| 7636. |
The term a_(r)^(t)+1/((r-1)^(r-1)) ge L , then which of the following can be the greatest vale of L |
|
Answer» `((a_(R)+)^(r))/(r^(r-1))` |
|
| 7637. |
Ifveca.vecb = vecc.veca for all vectors veca, then |
|
Answer» `vecabot(vecb-vecc)` |
|
| 7638. |
Find out the incorrect statement: |
|
Answer» The equation of tangent at 't' to the PARABOLA `y^(2)=4ax` |
|
| 7639. |
If A is a square matrix then A - A' is a …… matrix. |
|
Answer» SKEW symmetric |
|
| 7640. |
Calculate whenever possible,[[1,2],[2,1]][[3,1],[1,1]] |
|
Answer» SOLUTION :`[[1,2],[2,1]][[3,1],[1,1]]` `=[[1.3 +2.1""1.1+2.1],[2.3+1.1""2.1+1.1]]=[[5,3],[7,3]]` |
|
| 7641. |
Column 1: real valued function, Column-2: domain of the function, Column 3: range of the function. Match the following Column(s) (where [.] denotes the greatest integer function and {.} denotes fractional part function) Which of the following combination is correct? |
|
Answer» (IV)(i)(P) (II) `u=sin(In((sqrt(4-x^(2)))/(1-x)))+cos(In((sqrt(4-x^(2)))/(1-x)))` `:.0le (sqrt(4-x^(2)))/(1-x) lt oo` `-oo lt In ((sqrt(4-x^(2)))/(1-x))lt oo` So, `-sqrt(2) le u le sqrt(2)` (III) Let `|x+5|=t,G(t) in (0, 1/2]-{1/4}` `g(t)=((t-2))/((t-2)(t+2))` (IV) `thetalecos^(-1)xlepi` `-oo lt In (cos^(-1)x)le In pi lt 2` |
|
| 7642. |
Column 1: real valued function, Column-2: domain of the function, Column 3: range of the function. Match the following Column(s) (where [.] denotes the greatest integer function and {.} denotes fractional part function) Which of the following combination is correct? |
|
Answer» <P>(II)(iv)(P) (II) `U=sin(In((sqrt(4-x^(2)))/(1-x)))+cos(In((sqrt(4-x^(2)))/(1-x)))` `:.0le (sqrt(4-x^(2)))/(1-x) lt oo` `-oo lt In ((sqrt(4-x^(2)))/(1-x))lt oo` So, `-sqrt(2) LE u le sqrt(2)` (III) Let `|x+5|=t,g(t) in (0, 1/2]-{1/4}` `g(t)=((t-2))/((t-2)(t+2))` (IV) `thetalecos^(-1)xlepi` `-oo lt In (cos^(-1)x)le In pi lt 2` |
|
| 7643. |
Column 1: real valued function, Column-2: domain of the function, Column 3: range of the function. Match the following Column(s) (where [.] denotes the greatest integer function and {.} denotes fractional part function) Which of the following combination is correct? |
|
Answer» <P>(I)(iv)(P) (II) `u=sin(In((sqrt(4-x^(2)))/(1-x)))+cos(In((sqrt(4-x^(2)))/(1-x)))` `:.0LE (sqrt(4-x^(2)))/(1-x) LT oo` `-oo lt In ((sqrt(4-x^(2)))/(1-x))lt oo` So, `-sqrt(2) le u le sqrt(2)` (III) Let `|x+5|=t,g(t) in (0, 1/2]-{1/4}` `g(t)=((t-2))/((t-2)(t+2))` (IV) `thetalecos^(-1)xlepi` `-oo lt In (cos^(-1)x)le In pi lt 2` |
|
| 7644. |
If m,n are positive integers, maximum value of x^m(a-x)^n "in" (0,a) is |
|
Answer» `m^m(a-m)^N` |
|
| 7645. |
There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9)Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle")=(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3)Now, answer the following questions.Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is |
|
Answer» <P>`1//3`  Let A and B arrive at the place of their meeting 'a' minute and 'b' minute after 5 pm. Their meeting is possible only if `|a-b|le20` Clearly, `0le a le 60` and `0 le b le 60`.Therefore, a and b can be selected as an ordered pair (a,b) from the set `[0.60] xx [0.60]`.Alternatively, it is equivalent to select a POINT (a, b) from the square OPQR, where P is (60, 0) and R is (0, 60) in the Cartesian plane. Now, `|a-b| le 20 implies - 20 le a -b le 20` Therefore, points (a, b) satisfy the EQUATION `-20 le x - y le 20`.Hence, favorable condition is equivalent to selecting a point from the region BOUNDED by `y le x + 20` and `y ge x - 20`. Therefore, the required probability is `("Area of OABQCDO")/("Area of square OPQR")=([Ar(OPQR) - 2Ar(DeltaAPB)])/(Ar(OPQR))` `=(60 xx 60 - (2)/(2) xx 40 xx 40)/(60 xx 60) = (5)/(9)` |
|
| 7646. |
Two numbers are randomly selected from the first 100 natural numbers. The probability that the product of the numbers is divisible by 7 is |
|
Answer» 0 |
|
| 7647. |
If x+y+n=0, n gt 0 is a normal to the ellipse x^(3)+3y^(2)=3 and x^(2)+5y^(2)=5, then the point of intersection of these two lines satisfy the equation |
|
Answer» `(X^(2))/(64)-(y^(2))/(25)=1` |
|
| 7648. |
Evaluate the following determinants. [[2,3,1],[0,0,0],[-1,2,0]] |
|
Answer» SOLUTION :`[[2,3,1],[0,0,0],[-1,2,0]]`=0 as all the ENTRIES in the 2ND row are zero. |
|
| 7649. |
A coin whose faces are marked 3 and 4 is tossed five times. Find the probability of getting sum atleast 17. |
|
Answer» |
|
| 7650. |
Fora real number x let [x] denote the largest intger less than or equal to x. The smalleset positive integer n for which the integerint_(1)^(n)[x][sqrt(x]]dx exceeds 60 is- |
|
Answer» Solution :`I=underset(1)overset(2)intdx+underset(2)overset(3)int2dx+underset(3)overset(4)int3dx+underset(4)overset(5)int8dx+underset(5)overset(6)int10dx+underset(6)overset(7)int12dx+underset(7)overset(8)int14dx+underset(8)overset(9)int16dx+underset(9)overset(10)int27dx+underset(10)overset(11)int30dx+....` `I=1+2+3+8+10+12+14+16+=66` So n=9 |
|